Chika CE. Generalized multi-energy model for computing radiation treatment parameters on image domain and automated model-selection framework. World J Radiol 2026; 18(10): 126287 [DOI: 10.4329/wjr.126287]
Corresponding Author of This Article
Charles E Chika, PhD, Department of Mathematics, University of Nigeria, Obukpa Road, Nsukka 410001, Nigeria. charles.chika@unn.edu.ng
Research Domain of This Article
Radiology, Nuclear Medicine & Medical Imaging
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review-article
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Chika CE. Generalized multi-energy model for computing radiation treatment parameters on image domain and automated model-selection framework. World J Radiol 2026; 18(10): 126287 [DOI: 10.4329/wjr.126287]
World J Radiol. Oct 28, 2026; 18(10): 126287 Published online Oct 28, 2026. doi: 10.4329/wjr.126287
Generalized multi-energy model for computing radiation treatment parameters on image domain and automated model-selection framework
Charles E Chika
Charles E Chika, Department of Mathematics, University of Nigeria, Nsukka 410001, Nigeria
Author contributions: Chika CE conceptualized and wrote the manuscript as well as completed all the research and manuscript processes.
AI contribution statement: No AI tool was used.
Conflict-of-interest statement: The author declares that there is no known conflict of interest.
Corresponding author: Charles E Chika, PhD, Department of Mathematics, University of Nigeria, Obukpa Road, Nsukka 410001, Nigeria. charles.chika@unn.edu.ng
Received: July 30, 2026 Revised: September 2, 2026 Accepted: October 8, 2026 Published online: October 28, 2026 Processing time: 90 Days and 9.8 Hours
Abstract
This study developed a general n-energy mathematical model that predicts relative electron density (ρe), effective atomic number (Zef), mean excitation energy (I) and stopping power ratio (SPR) using computed tomography image, and developed an algorithm for best model selection. Mathematical proof is provided. Some numerical examples were carried out and the results were compared. The proposed method includes most of the existing methods as a special case. All the examples of the proposed method considered have modeling error that’s less than or equal to 0.85% and 0.89% for SPR and ρe, respectively, with mean error close to 0.00% and low median absolute error. The method was able to achieve modeling root mean square error of 0.85% and 1.61% for I and Zef, respectively, with some flexibility for improvement. The mathematical model showed to be more general by including most of the other existing models and presents a direction to formulating new ones. It shows little or no bias on prediction since it has mean error that is close to zero in almost all predictions and low median absolute error. The algorithm gives the leverage to select the best model, improve the model and automation.
Core Tip: This study presents a mathematical model for improving the precision of relative electron density, mean excitation energy, effective atomic number and stopping power ratio using computed tomography image. It exposes the need for machine learning algorithm that will help with best model selection. Based on the observation that the performance of the models differ based on the type of linear attenuation used (i.e., spectrally averaged linear attenuation or linear attenuation at effective energy), this study presents machine learning algorithm for best model selection. It also discusses the mathematical proof of the presented generalized model.
